Materials Science & Engineering A 564 (2013) 324–330

Contents lists available at SciVerse ScienceDirect

Materials Science & Engineering A

0921-50

http://d

n Corr

E-m

journal homepage: www.elsevier.com/locate/msea

Thermal barrier coating toughness: Measurement and identificationof a bridging mechanism enabled by segmented microstructure

Erin M. Donohue a,n, Noah R. Philips a, Matthew R. Begley a,b, Carlos G. Levi a,b

a Materials Department, University of California, Santa Barbara, United Statesb Mechanical Engineering Department, University of California, Santa Barbara, United States

a r t i c l e i n f o

Article history:

Received 18 September 2012

Received in revised form

27 November 2012

Accepted 30 November 2012Available online 8 December 2012

Keywords:

Toughness

Thermal barrier coatings

Yttria-stabilized zirconia

Fracture mechanisms

Crack bridging

93/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.msea.2012.11.126

esponding author. Fax: þ1 805 893 8486.

ail address: erin_donohue@engineering.ucsb.e

a b s t r a c t

Failure mechanisms in thermal barrier coatings (TBCs) often involve the propagation of delamination

cracks within the top coating. The work presented in this paper makes two principal contributions:

first, the development of a straightforward testing geometry and analysis approach enables the

accurate determination of the mode I fracture toughness of these coatings and second, the application

of the approach to technologically relevant coatings produces new insights into the impact of the dense

vertically cracked (DVC) microstructure on the toughness. Mode I toughness of air plasma-sprayed

8 wt% yttria-stabilized zirconia DVC TBCs is measured by sandwiching the freestanding coatings in a

modified double cantilever beam configuration. Digital image correlation measurements and finite

element analysis provide a pathway to quickly and accurately extract toughness values from

displacement data alone. Results show R-curve behavior and unexpectedly high steady-state toughness

values of Gss � 3002400 J=m2. The observation of this elevated toughness can be rationalized by a crack

bridging model that is consistent with the TBC’s starting microstructure and features of the fracture

surfaces.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

Thermal barrier coatings (TBCs) are key components of multi-layered thermal protection systems in gas turbines, which enablegreater fuel efficiency by allowing operation at increased tem-peratures [1,2]. The lifetime of a coating is often stronglydependent on its toughness, a property that determines theextent of various failure mechanisms [2], both intrinsic (e.g.thickening or rumpling of the thermally grown oxide [3–7]) andextrinsic (e.g. impact damage [8–11] and cracking due to moltensiliceous deposits [12–15]). Hence, predictions of coating dur-ability and design of future TBCs often rely critically on anaccurate assessment and understanding of toughness.

While the importance of measuring TBC toughness is clear[10,14], there are relatively few direct measurements on perti-nent microstructures [16–18]. (Indirect assessments on theintrinsic toughness of the appropriate composition, 8 wt% yttria-stabilized zirconia (8YSZ), include [19–21]). Coatings examined inthis article are produced by air plasma spray (APS) and containsegmented cracks in the thickness direction to provide greaterstrain tolerance upon thermal cycling (Fig. 1) [22–25]. Whilestandard APS coatings are highly porous to attain low thermal

ll rights reserved.

du (E.M. Donohue).

conductivity, the processing conditions to create the segmentedcracks cause the intervening material to have significantly lessporosity [26]. Referred to as dense vertically cracked (DVC)microstructures, these coatings can still maintain a sufficientlyhigh thermal gradient in operation [25,26]. In order to probe thebehavior of materials used in actual turbines, the difficult task offabricating suitable fracture specimens from thin, freestanding,ceramic coatings must be overcome.

Here, fracture experiments are conducted using a modifieddouble cantilever beam (DCB) geometry, where the TBC issandwiched between two steel beams and tested in displacementcontrol via wedge loading (Fig. 2). Quantification of R-curvebehavior is possible provided that (i) the crack tip can be correctlydetermined as a function of the beam deflection and (ii) theenergy release rate can be calculated accurately while accountingfor complicating factors such as the finite compliance of theceramic layer and transverse shear effects. These interrelatedchallenges are addressed by the combination of digital imagecorrelation (DIC) measurements and finite element (FE) analysis.

A key insight in the present approach, which facilitates theextraction of the crack tip location from DIC data, is that thecenterline of the beams experiences negative displacements justahead of the crack tip (Fig. 2). This feature is observed in both theFE results and analytical models of beams on finite-sized elasticfoundations (i.e. the length of the TBC in the sandwich). In bothanalyses, it is revealed that the distance between the onset of the

250 μm

Fig. 1. A cross-sectional view of an 8YSZ APS coating with a segmented microstructure comprising of through-thickness cracks that form an in-plane mud cracking pattern,

which define pillar-like features that enable the toughening mechanism discussed herein.

2δ CrackSi3N4 Wedge TBC CouponSteel Beams

h

δ

a

Displacementof neutral axiswith loading

s

Fig. 2. The DCB configuration (at bottom) and a schematic displacement trace of

the mid-line of the steel beam. The offset, s, indicates the location of the crack tip

relative to the onset of negative displacement (an effect of the compliant

foundation, exaggerated here, see also Fig. 4).

5 mm

0.80.4

0-0.4-0.8

δ (mm)

Fig. 3. In situ optical image of a speckled DCB specimen with overlaid displace-

ment contours from digital image correlation measurements.

E.M. Donohue et al. / Materials Science & Engineering A 564 (2013) 324–330 325

region of negative displacements and the crack tip location is,perhaps surprisingly, insensitive to reasonable variations in speci-men dimensions and TBC properties. Thus, a simple method isdeveloped to determine the crack length from DIC displacementmeasurements using a fitting procedure from FE results.

The toughness measurements elucidated by this approach revealR-curve behavior with steady-state values that are appreciablyhigher than the initiation toughness. This result and featuresobserved on the fracture surface strongly suggest that a crackbridging and pull-out mechanism, which develops as a conse-quence of the DVC microstructure, is responsible for the substantialimprovement of the TBC’s macroscopic resistance to fracture.

1 ETBC is actually an effective modulus that combines the contributions of the

TBC and the epoxy.

2. Experimental approach

Each DCB specimen was fabricated by sandwiching a TBCbetween two steel beams. Freestanding APS-DVC coatings (kindlyprovided by GE Energy), 25:4 mm� 25:4 mm� 1 mm, wereimpregnated with M-bond 610 epoxy (Vishay Micro-measure-ments) to minimize damage during sample preparation. A surfacegrinder with a 400 grit diamond wheel established flat, parallelsurfaces. The coatings were subsequently sectioned into beamsð25:4 mm� 6:35 mm� 1 mmÞ using a diamond blade and theepoxy was removed by oxidative decomposition in air at 700 1C.

To ensure adequate adhesion, the surfaces of two 304 stainlesssteel cantilevers ð63:5 mm� 6:35 mm� 3 mmÞ were first groundand then cleaned with acetone. A rubber-toughened adhesive film(FM-1000 from CYTEC Industries) was used to bond the YSZ to oneend of the beams. This high viscosity epoxy exhibited minimal

infiltration into the porous TBC. After curing at 170 1C, subject to apressure of 180 kPa, the epoxy was limited to an approximately60 mm thick film at the steel/TBC bond line. A small notch,introduced to the TBC using a diamond wafering blade, assistedcrack initiation. During the test, the far end of the specimen wassupported on a rigid base, with an intervening, soft metallic foil. Atthe loading end, a Si3N4 wedge, with a 151 half angle, waslubricated with graphite (Crown 8078). Samples were tested atroom temperature on a servo-hydraulic test frame (MTS 810)under displacement control.

Images of the specimen were captured at 15–20 s intervals sothat the displacement of the cantilevers, including at the locationof the wedge ðdÞ, could be measured using DIC (Fig. 3). Tofacilitate displacement mapping, the assembled specimen wasspeckled with black on white spray paint. After the experimentwas completed, the VIC2D DIC software from Correlated SolutionsInc. compared all images to an initial calibration image takenimmediately before testing commenced [27]. The area of interestwas defined as the entire speckled surface; the subset size was setto 51 pixels (to reduce noise), the step size was 5 pixels, and themagnification was typically 0:02870:002 mm=pixel. A series ofcorrelations on unstrained samples established the displacementresolution at better than 1 mm.

3. Calculations

Imaging limitations did not allow for a precise optical deter-mination of the crack tip location and compliance methods wereinaccurate for the chosen geometry, resulting in an overestima-tion of energy release rate. Numerical analysis, through FEsimulations in ABAQUS/CAE, facilitated accounting for complexinteractions such as the extent of deviations from Bernoulli–Eulerbeam theory (for one, shear effects at the crack tip) and thepresence of the compliant foundation [28–30]. As such, a 2D FEmodel was utilized to provide values of energy release rate for aset of geometric (lengths: Lsteel, LTBC and thicknesses: hsteel, hTBC)and elastic (Esteel, ETBC

1) parameters, a given crack length (a), andopening displacement at the load point (d).

E.M. Donohue et al. / Materials Science & Engineering A 564 (2013) 324–330326

The information extracted from the experiment was thedisplacement as a function of position along the mid-line of thesteel beam, collected as d increased. There remained a challengein translating the experimental data, which provided values of dbut not a, into FE inputs. Given a rigid foundation, such as inconventional beam theory, the crack tip’s position is that of thezero deflection of the beam. However, using this displacementmetric to determine crack length results in erroneously highvalues when a compliant foundation is present. For a beam onan elastic foundation, the zero crossing and succeeding region ofnegative displacement (Fig. 2) are useful if a relationship betweenthe location of these features and the crack tip is known. A FEstudy was performed to determine the sensitivity of the zerocrossing on specimen dimensions and properties.

A symmetric FE model was created with physical dimensionsmatching those of half the experimental specimen (one steelbeam and 1/2 thickness of the TBC), and meshes were tested forconvergence. An independent epoxy layer was not included;instead, adjacent nodes in the steel and TBC were tied. Thecontribution of the epoxy’s low modulus was accounted for bycombining it with the TBC’s elastic properties into an effectiveuniaxial modulus, ETBC. Boundary conditions prevented rigid bodytranslations of the steel beam. Meshes of the steel and TBCcontained 288� 15 and 1320� 26 plane stress elements, respec-tively. The elastic modulus of the steel beam was defined to be193 GPa and an estimated modulus was assigned to the TBC.Since the properties of the heterogeneous DVC coating are notfully understood, the modulus was used as a parameter in thesensitivity study. Ten cases were analyzed, with ETBC ranging from102200 GPa, where the upper bound corresponds to the modulusof dense 8YSZ and the lower bound to the modulus of a laminatedcomposite of 10% epoxy and 90% dense zirconia [31–33]. Arepresentative load point displacement of d¼ 0:5 mm was usedfor the entire sensitivity study; the elastic analysis makes thespecific value chosen immaterial, as displacements will scalelinearly with the load point displacement. The crack grew fromthe start of the TBC in increments of 0:1 � LTBC , and at each cracklength, displacements along the midline of the steel beam wererecorded.

As expected, plots of displacement as a function of positionexhibited a region of negative displacement due to the elasticfoundation, as illustrated schematically in Fig. 2. Since cracklength was prescribed in these FE simulations, its value could berelated to the characteristic features of the region of negativedisplacement, such as its onset, length, or minimum value. It wasdetermined that it is most reliable to use the position where thebeam displacement is zero, preceding the displacements becom-ing negative. The distance between the location of the crack tipand the onset of the region of negative displacements is hence-forth referred to as s (Fig. 2). The sensitivity study examined hows is influenced by parameters in the FE model. Knowledge ofvariation in s was necessary in order to apply this offset toexperimental data and be confident in the extracted values ofcrack length.

For a given set of dimensions and material properties, therewas a characteristic value of s which was constant until the crackreached the last � 30% of the length of the TBC.2 Uncertainty in s

arose from variability in parameters that are not well known oreasily measured, specifically the TBC modulus. As ETBC was variedfrom 102200 GPa, s was consistently within the range of1:1422:31 mm for the chosen geometry. Remembering that crack

2 Knowledge of the value of s at longer crack lengths has been characterized,

but was not relevant since the experimental data sampling rate was too low to

capture the rapid propagation of the crack once it approached the end of the beam.

length was measured from the load point, this range in s

translated to a maximum of a 3.3% difference between possiblecrack lengths. While the behavior near the crack tip was heavilyinfluenced by the compliant foundation, the minimal sensitivityof s (and by extension, crack length) to modulus within theapplicable range, was due to the bending stiffness of the steelbeams dominating the deformation of the rest of the specimen.As such, knowledge of the exact TBC modulus was not critical.Since utilization of the sensitivity study’s results requires experi-mental data, this procedure is described in Section 4. As will beillustrated, using ETBC ¼ 25 GPa as an effective modulus of theTBC/epoxy bilayer resulted in a good match between the simula-tions and experiments; the characteristic offset value for theseconditions is s¼ 1:77 mm.

4. Results

Displacement data was extracted from the centerline of thebeams in all images using the crack opening displacement (COD)tool in the VIC2D program. From each of these data sets, aMathematica script discerned the displacement at the load point,d, and the position of the first zero crossing. The s offset value wassubtracted from this position to determine the location of thecrack tip, a. Thus, there were (d, a) pairs associated with eachimage, and these pairs were used as inputs for the FE simulations.To verify that the FE model was accurately representing theexperiment, each resulting displacement trace from the simula-tion was then compared to that from the image it represented(Fig. 4). The close match to what was seen experimentally for thesame value of d suggests that the s offset calculation had correctlypredicted the crack length.

The macroscopic energy release rate (i.e. driving force) wascalculated from the FE results using the well established J-integral[34] (available as a tool in ABAQUS), under the assumption thatthe fracture process zone is small relative to the crack length.Plotting these TBC toughness values against the calculated cracklengths produced an R-curve.

Nine specimens were fabricated from three standard DVCcoatings (three each), and out of these samples, there were sixsuccessful experiments where the crack propagated primarilywithin the TBC. In three cases, the experiment was ideal (thesecracks did not deviate into the TBC/epoxy interface); this behavioroccurred in one specimen from each of the three coupons(Fig. 5a). Crack growth resistance increased for extensions ofabout 5 mm and then attained a steady-state of Gss � 3002

400 J=m2. The other successful experiments exhibited a fewdiscrete zones of delamination between the coating and epoxy(Fig. 5b), but the majority of the failure did occur within the TBC.Error, represented in Fig. 5c, includes uncertainties from themeasurements of position along the steel beam and calibrationvalue, noise in the DIC data, and slight deviations from the idealspecimen geometry that was used in the sensitivity studydetermination of the offset, s. To demonstrate the insensitivityof the measured toughness to ETBC and s, multiple simulationswere run for one experimental data set. There was not asignificant difference in steady-state values, regardless of theexact value of ETBC, within the applicable range of 102200 GPa,or whether s was appropriately adjusted to match the TBCmodulus (Fig. 6).

The steady-state energy release rates from the specimens withsome adhesive failure fell within the range defined by the moreideal tests. Furthermore, the toughness behavior of the specimensfrom each coupon followed similar trajectories. The range insteady-state values was due to typical variations in microstructure

0.5

1.0

0

Dis

plac

emen

t (μm

)

-0.5

0

0.5

605040

Dis

plac

emen

t (μm

)

Position (mm)

Fig. 4. (a) Displacement of the steel beam’s neutral axis in the early stage of crack

growth and (b) as the crack nears the end of the beam. In both cases, the traces of

simulation results are overlaid on the experimental data points. The compressive

region ahead of the crack tip is a manifestation of the significant compliance in the

foundation of the beam, i.e. the TBC layer.

0 5 10 150

100

200

300

400

Crack Extension, ∆a (mm)

Ene

rgy

Rel

ease

Rat

e, G

(J/m

2 )

Coupon 1

Coupon 2

Coupon 3

Fig. 5. (a) Measurement of the energy release rate as the crack advances exhibits R-curv

of partial adhesive failure, repeatable results are attained with toughness values falling e

uncertainties, representative values shown here for a single sample, are less than the

E.M. Donohue et al. / Materials Science & Engineering A 564 (2013) 324–330 327

across different coatings, rather than small variations that arisefrom uncontrolled factors in the test.

Complementary fracture surfaces (Fig. 7a) revealed extensivepull-out of the DVC columns. Visual inspection showed thatpillars were on the fracture surface associated with the top ofthe coating (Fig. 7b), while sockets were present on the substrateside. Reminiscent of fiber pull-out in composites [35], it wassurmised that the associated frictional dissipation contributedsignificantly to the toughness. Features on these surfaces werecharacterized by optical profilometry (Veeco Wyko NT100).

1000

100

200

300

400

∆a (mm)

G (J/m2)

Partial Adhesive Failure

155 1000

100

200

300

∆a (mm)

G (J/m2)

RepresentativeUncertainties

Coupon 2

e behavior, with steady-state toughness values of Gss � 3002400 J=m2. (b) In cases

ntirely within the range established by the more ideal experiments. (c) Calculation

experimental scatter.

10

2001.77

1.14

1.77

2.31

ETBC(GPa)

s(mm)

G(J/m2)

15 200 5 100

100

200

300

400

Ene

rgy

Rel

ease

Rat

e, G

(J/m

2 )

Crack Extension, ∆a (mm)

350

400

325

375

Fig. 6. Toughness values are insensitive to plausible variations of ETBC and s.

Multiple simulations on one experimental data set (TBC coupon #2 in Fig. 5) result

in steady-state toughness values within experimental scatter.

0

800 mm

2 mm

5 mm

Fig. 7. Visual evidence of a bridging mechanism. (a) Optical micrograph of

complementary fracture surfaces of a DVC coating after a DCB test with high-

lighted pillars and corresponding sockets. (b) Surface topography produced by

profilometry, including a detail of a small region containing a pillar with a

diameter approximately equivalent to the DVC spacing and an approximate height

of half the coating thickness.

E.M. Donohue et al. / Materials Science & Engineering A 564 (2013) 324–330328

In order to probe the operability of the ferroelastic mechanismconsidered responsible for the superior toughness of tetragonal7-8YSZ, a comparison was made between X-ray diffraction (XRD)measurements (Panalytical XPERT MPD Powder Diffractometer)performed on a fracture surface and on the top surface of anunmodified TBC. A substantial change in relative intensitiesbetween orthogonal reflections in the {002}, {113}, and {004}systems, indicative of an enhanced population of [001] tetragonaldomains oriented normal to the surface, was evident afterfracture (Fig. 8) [36].

5. Discussion

The salient finding of this investigation, beyond the demon-stration that the toughness of porous, microcracked coatings canbe rigorously quantified using a DCB/DIC approach, is the obser-vation of toughness values much higher than those measured byconventional microindentation methods on dense samples of thesame composition, which are of order G0 � 4075 J=m2 [20].3 Thiselevated steady-state toughness can be rationalized by a crack

3 The comparison is made here only to highlight the order of magnitude of the

difference since the microindentation value is often cited as the intrinsic tough-

ness of the dense material. The latter, however, may vary depending on composi-

tion and microstructure [21,20,37,38] but there is no precedent for the values

bridging and pull-out micromechanical phenomenon wherein theDVC columns act in a manner similar to aligned fibers in acomposite [35,39]. In essence, the mechanism is envisaged toproceed as follows (Fig. 9): the crack propagates sampling thestrength of the putative pillars (Fig. 9a), fracturing the weakerones and deflecting at the open boundaries adjacent to thestronger pillars (Fig. 9b), which form bridges across the crack.As the crack continues to open, the stress in any given bridgingpillar eventually meets the fracture condition for a critical flaw,often causing failure remote from the crack plane [35]. Thosepillars then pull out of their sockets with substantial frictionaldissipation at their boundaries [35,40]. Relative displacements ofthe pillars and the tractions they exert on the crack faces aregoverned by the friction stress, t, at the column interfaces(Fig. 9c).

The analysis by Suo et al. [41] on the R-curves resulting frombridging mechanisms is used to calculate the effective bridgingstress (s0) and the critical opening for loss of bridging traction(d0). These two quantities, coupled with the pillar geometry, canbe used to estimate the friction stress through a standard shearlag analysis of pillar pullout. (This analysis must yield plausiblevalues of t to substantiate the above mechanism.) Since theR-curve produced from the current work resembles the case Suopresents for application of a pure moment, which achievessteady-state, the equations for rigid plastic bridging correspond-ing to that configuration were employed. The superposition ofstresses and displacements arising from the applied moment andthe bridging mechanism produces the following expressions:

ffiffiffiffiffiffiffiGss

p¼

ffiffiffiffiffiffiG0

pþ

a1

2

ffiffiffiCp

L2sss0 ð1Þ

d0 ¼ a1L2ss

ffiffiffiffiffiffiffiffiffiCGss

p�

a21

4L4

ssCs0 ð2Þ

where Gss is the steady-state toughness, G0 is the intrinsictoughness, a1 is a computed coefficient dependent on specimengeometry and stiffness, C is the beam compliance, and Lss is thesteady-state bridging zone size. Values for Gss, G0, and Lss areextracted from G vs a curves (Fig. 5), such that the bridgingparameters d0 and s0 can be inferred from these equations for agiven traction-displacement bridging law.

Regardless of whether the rigid plastic or softening bridging isassumed for the five samples analyzed by surface profilometry, d0

is calculated to be 40720 mm. The features of one fracturesurface were measured individually, and the average pillar heightis 3–4 times greater than the calculated d0 values. It is hypothe-sized that the initially torturous interfaces of the intact DVCpillars lead to some comminution of the material during pullout,contributing to the sliding stress and amount of frictional dis-sipation. After sliding about 40 mm, the interfaces become smoothresulting in decreased contact with each other and effective lossof bridging traction.

While d0 exhibits no dependence on whether the bridging isrigid plastic or softening, s0 is affected, with a mean value of5:7 MPa in the former case and 11:3 MPa in the latter. To evaluatewhether or not such a bridging stress is plausible, it is instructiveto calculate the effective sliding stress between pillars that wouldhave to be present to generate stresses of this magnitude.Assuming a constant frictional sliding stress during pull-out andsmall displacements, equilibrium implies [35,40,42]

s0 ¼2ht

Rf ð3Þ

(footnote continued)

reported here. The relevance of the intrinsic toughness to the fracture process is

addressed later in the discussion.

2R

hτ

σ<σο250 μm

Fig. 9. Cross-sectional views of the same portion of a TBC (a) before (with the eventual crack path indicated by the dashed line) and (b) after fracture reveal the

relationship between the vertical cracks in the starting microstructure and the size of a pillar. (c) Illustration of the development of crack bridges and pull-out in a DVC

microstructure. The propagating crack follows the path of least resistance, occasionally deflecting at the DVCs and creating pillars in the wake. Upon failure, the pillars

undergo frictional pull-out, contributing to an increase in toughness.

As-deposited

FractureSurface002 113 004

Nor

mal

ized

Inte

nsity

400131200

0.0

1.0

2θ 0.0

1.0

34.5 35 59 60 73 740.0

1.0

Fig. 8. XRD showing the redistribution in the relative population of tetragonal domain orientation on the fracture surface is suggestive of ferroelastic switching.

The population of domains with their c-axis oriented along the crack normal increases during the fracture process.

E.M. Donohue et al. / Materials Science & Engineering A 564 (2013) 324–330 329

where R and h are the nominal radius and height, respectively, ofthe pillars, f is the area fraction of the fracture surface thatexperiences pull-out and t is the frictional sliding stress. Thisexpression for s0 can be further simplified by noting that the areafraction of pillars can be expressed as

f ¼np R2

Að4Þ

where A is the area of the crack plane and n is the number ofpillars on the surface. The bridging stress is then given by

s0 ¼n2p Rht

Að5Þ

Optical profilometry data (Fig. 7b) provides values for the totalarea of the fracture surface (including both the sides and plateausof the pillars) and the projected area, A; the difference betweenthese measured values is equal to the area of the pillar sides,which is the relevant surface for frictional pull-out (n2pRh). Usingthe calculated s0 values, it is determined that t� 5238 MPa, witha mean of 13 MPa. While direct measurements of pull-out stressare required to determine the sliding stress, this inferred frictionstress is quite plausible, considering values calculated for othersystems [43,44]. The consistency between the deduced pull-outdistance and height of the pillars, as well as a reasonable level ofsliding stress, lends strong support to the hypothesis of africtional bridging mechanism.

Concomitant to the bridging mechanism, ferroelastic switchingmay provide additional toughening that also manifests as R-curvebehavior, due to the evolution of a process zone surrounding thecrack tip. One may estimate that the steady-state increase in

toughness associated purely with switching is of the order of thatobserved between dense compacts of cubic and tetragonal ðt0Þzirconia, � 40 J=m2 [20,21], which is much less than the enhance-ment observed in the experiments. The interplay between thebridging mechanism associated with the columnar microstructureand the ferroelastic contribution arising from the switching oftetragonal domains in the process zone is not fully understood atthis time. One may hypothesize, however, that a higher intrinsictoughness would increase the stress necessary to advance thecrack tip even in the absence of bridging effects and/or, moreimportantly, increase the average pull-out length and the bridgingeffect. In essence, for a given flaw distribution a higher intrinsictoughness would, in principle, require sampling a larger volume ofmaterial in each pillar before activating a crack, or if the pillar isalready broken at a distance away from the main crack plane, itcan withstand the pull-out process without fracturing again underthe applied stress. The key point is that determination of bridgingeffectiveness requires considerations of the microstructural seg-mentation, the intrinsic toughness, and the flaw distribution.Research is in progress to help elucidate these issues and will bereported in future publications.

6. Conclusion

A refined DCB experimental procedure and analysis is developedand this high-fidelity method can be exploited to accurately measurethe toughness of freestanding thin films. The measured mode Itoughness of APS coatings with the DVC microstructure has anunexpectedly high steady-state value of 3002400 J=m2. Auspiciously,

E.M. Donohue et al. / Materials Science & Engineering A 564 (2013) 324–330330

this elevated energy release rate is consistent with tougheningmechanisms based on bridging and frictional dissipation, enabledby a combination of the microstructural architecture and an increasedintrinsic toughness through ferroelastic switching, which correspondto features observed on the fracture surfaces. Thus, it is inferred thatthe segmented microstructure has a significant and positive impacton the long-crack toughness of TBCs.

Acknowledgments

This investigation was financially supported under GrantsDMR-0605700 and DMR-1105672 from the National ScienceFoundation. Additional support for EMD through the GAANNfellowship program from the Department of Education is grate-fully acknowledged. The research made use of the UCSB MRLCentral Facilities, which are supported by the MRSEC Programof the NSF under Award No. DMR-1121053; a member of theNSF-funded Materials Research Facilities Network (http://www.mrfn.org). The authors are grateful to Drs. D.M. Lipkin (GE-GRC) andC.A. Johnson (GE-GRC) for insightful discussions, to Dr. W.A. Nelson(GE-Energy) for providing the coatings examined in this study, andespecially to the late professor A.G. Evans who was instrumental inmotivating this work.

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